Trigonometry- Sin, Cos and Tan

Introduction to Trigonometry

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
The basic trigonometric functions are sine (sin), cosine (cos), and tangent (tan).
These functions are useful for finding the sides and angles of right-angled triangles.

The sine of an angle (sin) in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
The cosine of an angle (cos) in a right-angled triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
The tangent of an angle (tan) in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

A useful way to remember how to use sin, cos, and tan is to remember SOHCAHTOA.
- This stands for Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent.
This can be a helpful mnemonic when applying these functions in calculations.

Trigonometric functions are used to find unknown sides or angles in a right-angled triangle.
To calculate an unknown side length, we need to know the size of one of the non-right angles and the length of one of the other sides.
To find an unknown angle, we need to know the length of two sides.
The inverse trigonometric functions sin-1, cos-1, tan-1 allows us to find an unknown angle from known side lengths.

Trigonometry is widely used in real life, from designing buildings and bridges to understanding waves and sound frequencies.
It is central to physics, engineering, music, telecommunications, and a range of other areas.
Developing a solid understanding of trigonometry functions and how to apply them is therefore of immense practical use.

As with Pythagoras’ theorem, the key to becoming proficient at trigonometry is practice.
Methodical and frequent revision and problem-solving can gradually build up your confidence and proficiency.
Work through a variety of problems to understand how these concepts are applied and formulate your own strategies and tricks to remember them.
If a problem seems complex, remember to break it down step by step, and don’t hesitate to revisit the concept if needed.
And finally, remember, learning is filled with mistakes and misunderstandings, so keep trying, keep learning and keep improving!